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The Fisher-Wright model with deterministic seed bank and selection

Bendix Koopmann, Johannes Müller, Aurélien Tellier, Daniel Živković
doi: https://doi.org/10.1101/035246
Bendix Koopmann
Center for Mathematics, Technische Universität München, 85748 Garching, Germany E-mail: ·
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  • For correspondence: bendix.koopmann@mytum.de johannes.mueller@mytum.de
Johannes Müller
Center for Mathematics, Technische Universität München, 85748 Garching, Germany E-mail: ·
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  • For correspondence: bendix.koopmann@mytum.de johannes.mueller@mytum.de
Aurélien Tellier
Section of Population Genetics, Center of Life and Food Sciences Weihenstephan, Technische Universität München, 85354 Freising, Germany E-mail:
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  • For correspondence: tellier@wzw.tum.de
Daniel Živković
Section of Evolutionary Biology, Department of Biology, Ludwig-Maximilians-Universität München, 82152 Martinsried, Germany E-mail:
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  • For correspondence: zivkovic@bio.lmu.de
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Abstract

Seed banks are a common characteristics to many plant species, which allow storage of genetic diversity in the soil as dormant seeds for various periods of time. We investigate an above-ground population following a Fisher-Wright model with selection coupled with a deterministic seed bank assuming the length of the seed bank is kept constant and the number of seeds is large. To assess the combined impact of seed banks and selection on genetic diversity, we derive a general diffusion model. We compute the equilibrium solution of the site-frequency spectrum and derive the times to fixation of an allele with and without selection. Finally, it is demonstrated that seed banks enhance the effect of selection onto the site-frequency spectrum while slowing down the time until the mutation-selection equilibrium is reached.

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Posted December 24, 2015.
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The Fisher-Wright model with deterministic seed bank and selection
Bendix Koopmann, Johannes Müller, Aurélien Tellier, Daniel Živković
bioRxiv 035246; doi: https://doi.org/10.1101/035246
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The Fisher-Wright model with deterministic seed bank and selection
Bendix Koopmann, Johannes Müller, Aurélien Tellier, Daniel Živković
bioRxiv 035246; doi: https://doi.org/10.1101/035246

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